Multiwavelength observations are essential to constrain physical parameters of the blazars observed by Fermi/LAT. Among the 187 AGN significantly detected in public INTEGRAL data above 20 keV by the imager IBIS/ISGRI, 20 blazars were detected. 15 of these sources allowed significant spectral extraction. They show hard X-ray spectra with an average photon index of 2.1+-0.1 and a hard X-ray luminosity of L(20-100 keV) = 1.3e46 erg/s. 15 of the INTEGRAL blazars are also visible in the first 16 months of the Fermi/LAT data, thus allowing to constrain the inverse Compton branch in these cases. Among others, we analyse the LAT data of four blazars which were not included in the Fermi LAT Bright AGN Sample based on the first 3 months of the mission: QSO B0836+710, H 1426+428, RX J1924.8-2914, and PKS 2149-306. Especially for blazars during bright outbursts, as already observed simultaneously by INTEGRAL and Fermi (e.g. 3C 454.3 and Mrk 421), INTEGRAL provides unique spectral coverage up to several hundred keV. We present the spectral analysis of INTEGRAL and Fermi data and demonstrate the potential of INTEGRAL observations of Fermi detected blazars in outburst by analysing the combined data set of the persistent radio galaxy Cen A.
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